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Properties

Label 2664.2.a.f.1.1
Level $2664$
Weight $2$
Character 2664.1
Self dual yes
Analytic conductor $21.272$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2664,2,Mod(1,2664)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2664, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2664.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2664 = 2^{3} \cdot 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2664.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(21.2721470985\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 296)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2664.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{5} +1.00000 q^{7} +O(q^{10})\) \(q+2.00000 q^{5} +1.00000 q^{7} -1.00000 q^{11} -6.00000 q^{13} +4.00000 q^{17} -8.00000 q^{19} -6.00000 q^{23} -1.00000 q^{25} -2.00000 q^{29} -4.00000 q^{31} +2.00000 q^{35} -1.00000 q^{37} -7.00000 q^{41} +2.00000 q^{43} -9.00000 q^{47} -6.00000 q^{49} +3.00000 q^{53} -2.00000 q^{55} +12.0000 q^{59} +4.00000 q^{61} -12.0000 q^{65} -7.00000 q^{71} +7.00000 q^{73} -1.00000 q^{77} -3.00000 q^{83} +8.00000 q^{85} +12.0000 q^{89} -6.00000 q^{91} -16.0000 q^{95} -8.00000 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 2.00000 0.894427 0.447214 − 0.894427i \(-0.352416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964 0.188982 − 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.00000 −0.301511 −0.150756 − 0.988571i \(-0.548171\pi\)
−0.150756 + 0.988571i \(0.548171\pi\)
\(12\) 0 0
\(13\) −6.00000 −1.66410 −0.832050 − 0.554700i \(-0.812833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.00000 0.970143 0.485071 − 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) 0 0
\(19\) −8.00000 −1.83533 −0.917663 − 0.397360i \(-0.869927\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −6.00000 −1.25109 −0.625543 − 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 − 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 − 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.00000 0.338062
\(36\) 0 0
\(37\) −1.00000 −0.164399
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −7.00000 −1.09322 −0.546608 − 0.837389i \(-0.684081\pi\)
−0.546608 + 0.837389i \(0.684081\pi\)
\(42\) 0 0
\(43\) 2.00000 0.304997 0.152499 − 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −9.00000 −1.31278 −0.656392 − 0.754420i \(-0.727918\pi\)
−0.656392 + 0.754420i \(0.727918\pi\)
\(48\) 0 0
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 3.00000 0.412082 0.206041 − 0.978543i \(-0.433942\pi\)
0.206041 + 0.978543i \(0.433942\pi\)
\(54\) 0 0
\(55\) −2.00000 −0.269680
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 12.0000 1.56227 0.781133 − 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) 0 0
\(61\) 4.00000 0.512148 0.256074 − 0.966657i \(-0.417571\pi\)
0.256074 + 0.966657i \(0.417571\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −12.0000 −1.48842
\(66\) 0 0
\(67\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −7.00000 −0.830747 −0.415374 − 0.909651i \(-0.636349\pi\)
−0.415374 + 0.909651i \(0.636349\pi\)
\(72\) 0 0
\(73\) 7.00000 0.819288 0.409644 − 0.912245i \(-0.365653\pi\)
0.409644 + 0.912245i \(0.365653\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −3.00000 −0.329293 −0.164646 − 0.986353i \(-0.552648\pi\)
−0.164646 + 0.986353i \(0.552648\pi\)
\(84\) 0 0
\(85\) 8.00000 0.867722
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 12.0000 1.27200 0.635999 − 0.771690i \(-0.280588\pi\)
0.635999 + 0.771690i \(0.280588\pi\)
\(90\) 0 0
\(91\) −6.00000 −0.628971
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −16.0000 −1.64157
\(96\) 0 0
\(97\) −8.00000 −0.812277 −0.406138 − 0.913812i \(-0.633125\pi\)
−0.406138 + 0.913812i \(0.633125\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 17.0000 1.69156 0.845782 − 0.533529i \(-0.179135\pi\)
0.845782 + 0.533529i \(0.179135\pi\)
\(102\) 0 0
\(103\) 2.00000 0.197066 0.0985329 − 0.995134i \(-0.468585\pi\)
0.0985329 + 0.995134i \(0.468585\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.00000 0.386695 0.193347 − 0.981130i \(-0.438066\pi\)
0.193347 + 0.981130i \(0.438066\pi\)
\(108\) 0 0
\(109\) 16.0000 1.53252 0.766261 − 0.642529i \(-0.222115\pi\)
0.766261 + 0.642529i \(0.222115\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −2.00000 −0.188144 −0.0940721 − 0.995565i \(-0.529988\pi\)
−0.0940721 + 0.995565i \(0.529988\pi\)
\(114\) 0 0
\(115\) −12.0000 −1.11901
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 4.00000 0.366679
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) −17.0000 −1.50851 −0.754253 − 0.656584i \(-0.772001\pi\)
−0.754253 + 0.656584i \(0.772001\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) −8.00000 −0.693688
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 14.0000 1.19610 0.598050 − 0.801459i \(-0.295942\pi\)
0.598050 + 0.801459i \(0.295942\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 − 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 6.00000 0.501745
\(144\) 0 0
\(145\) −4.00000 −0.332182
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 9.00000 0.737309 0.368654 − 0.929567i \(-0.379819\pi\)
0.368654 + 0.929567i \(0.379819\pi\)
\(150\) 0 0
\(151\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −8.00000 −0.642575
\(156\) 0 0
\(157\) 19.0000 1.51637 0.758183 − 0.652042i \(-0.226088\pi\)
0.758183 + 0.652042i \(0.226088\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −6.00000 −0.472866
\(162\) 0 0
\(163\) −22.0000 −1.72317 −0.861586 − 0.507611i \(-0.830529\pi\)
−0.861586 + 0.507611i \(0.830529\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −12.0000 −0.928588 −0.464294 − 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3.00000 0.228086 0.114043 − 0.993476i \(-0.463620\pi\)
0.114043 + 0.993476i \(0.463620\pi\)
\(174\) 0 0
\(175\) −1.00000 −0.0755929
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 22.0000 1.64436 0.822179 − 0.569230i \(-0.192758\pi\)
0.822179 + 0.569230i \(0.192758\pi\)
\(180\) 0 0
\(181\) −23.0000 −1.70958 −0.854788 − 0.518977i \(-0.826313\pi\)
−0.854788 + 0.518977i \(0.826313\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2.00000 −0.147043
\(186\) 0 0
\(187\) −4.00000 −0.292509
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) −10.0000 −0.719816 −0.359908 − 0.932988i \(-0.617192\pi\)
−0.359908 + 0.932988i \(0.617192\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −7.00000 −0.498729 −0.249365 − 0.968410i \(-0.580222\pi\)
−0.249365 + 0.968410i \(0.580222\pi\)
\(198\) 0 0
\(199\) −14.0000 −0.992434 −0.496217 − 0.868199i \(-0.665278\pi\)
−0.496217 + 0.868199i \(0.665278\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −2.00000 −0.140372
\(204\) 0 0
\(205\) −14.0000 −0.977802
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 8.00000 0.553372
\(210\) 0 0
\(211\) 9.00000 0.619586 0.309793 − 0.950804i \(-0.399740\pi\)
0.309793 + 0.950804i \(0.399740\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 4.00000 0.272798
\(216\) 0 0
\(217\) −4.00000 −0.271538
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −24.0000 −1.61441
\(222\) 0 0
\(223\) 25.0000 1.67412 0.837062 − 0.547108i \(-0.184271\pi\)
0.837062 + 0.547108i \(0.184271\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −24.0000 −1.59294 −0.796468 − 0.604681i \(-0.793301\pi\)
−0.796468 + 0.604681i \(0.793301\pi\)
\(228\) 0 0
\(229\) −5.00000 −0.330409 −0.165205 − 0.986259i \(-0.552828\pi\)
−0.165205 + 0.986259i \(0.552828\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2.00000 0.131024 0.0655122 − 0.997852i \(-0.479132\pi\)
0.0655122 + 0.997852i \(0.479132\pi\)
\(234\) 0 0
\(235\) −18.0000 −1.17419
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −10.0000 −0.646846 −0.323423 − 0.946254i \(-0.604834\pi\)
−0.323423 + 0.946254i \(0.604834\pi\)
\(240\) 0 0
\(241\) −30.0000 −1.93247 −0.966235 − 0.257663i \(-0.917048\pi\)
−0.966235 + 0.257663i \(0.917048\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −12.0000 −0.766652
\(246\) 0 0
\(247\) 48.0000 3.05417
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −26.0000 −1.64111 −0.820553 − 0.571571i \(-0.806334\pi\)
−0.820553 + 0.571571i \(0.806334\pi\)
\(252\) 0 0
\(253\) 6.00000 0.377217
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −12.0000 −0.748539 −0.374270 − 0.927320i \(-0.622107\pi\)
−0.374270 + 0.927320i \(0.622107\pi\)
\(258\) 0 0
\(259\) −1.00000 −0.0621370
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −13.0000 −0.801614 −0.400807 − 0.916162i \(-0.631270\pi\)
−0.400807 + 0.916162i \(0.631270\pi\)
\(264\) 0 0
\(265\) 6.00000 0.368577
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 6.00000 0.365826 0.182913 − 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) 0 0
\(271\) −9.00000 −0.546711 −0.273356 − 0.961913i \(-0.588134\pi\)
−0.273356 + 0.961913i \(0.588134\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.00000 0.0603023
\(276\) 0 0
\(277\) 12.0000 0.721010 0.360505 − 0.932757i \(-0.382604\pi\)
0.360505 + 0.932757i \(0.382604\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 20.0000 1.19310 0.596550 − 0.802576i \(-0.296538\pi\)
0.596550 + 0.802576i \(0.296538\pi\)
\(282\) 0 0
\(283\) 8.00000 0.475551 0.237775 − 0.971320i \(-0.423582\pi\)
0.237775 + 0.971320i \(0.423582\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −7.00000 −0.413197
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −6.00000 −0.350524 −0.175262 − 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 0 0
\(295\) 24.0000 1.39733
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 36.0000 2.08193
\(300\) 0 0
\(301\) 2.00000 0.115278
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 8.00000 0.458079
\(306\) 0 0
\(307\) 29.0000 1.65512 0.827559 − 0.561379i \(-0.189729\pi\)
0.827559 + 0.561379i \(0.189729\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −24.0000 −1.36092 −0.680458 − 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 0 0
\(313\) 18.0000 1.01742 0.508710 − 0.860938i \(-0.330123\pi\)
0.508710 + 0.860938i \(0.330123\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 10.0000 0.561656 0.280828 − 0.959758i \(-0.409391\pi\)
0.280828 + 0.959758i \(0.409391\pi\)
\(318\) 0 0
\(319\) 2.00000 0.111979
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −32.0000 −1.78053
\(324\) 0 0
\(325\) 6.00000 0.332820
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −9.00000 −0.496186
\(330\) 0 0
\(331\) −22.0000 −1.20923 −0.604615 − 0.796518i \(-0.706673\pi\)
−0.604615 + 0.796518i \(0.706673\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −9.00000 −0.490261 −0.245131 − 0.969490i \(-0.578831\pi\)
−0.245131 + 0.969490i \(0.578831\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 4.00000 0.216612
\(342\) 0 0
\(343\) −13.0000 −0.701934
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −22.0000 −1.18102 −0.590511 − 0.807030i \(-0.701074\pi\)
−0.590511 + 0.807030i \(0.701074\pi\)
\(348\) 0 0
\(349\) −26.0000 −1.39175 −0.695874 − 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 36.0000 1.91609 0.958043 − 0.286623i \(-0.0925328\pi\)
0.958043 + 0.286623i \(0.0925328\pi\)
\(354\) 0 0
\(355\) −14.0000 −0.743043
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 25.0000 1.31945 0.659725 − 0.751507i \(-0.270673\pi\)
0.659725 + 0.751507i \(0.270673\pi\)
\(360\) 0 0
\(361\) 45.0000 2.36842
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 14.0000 0.732793
\(366\) 0 0
\(367\) −16.0000 −0.835193 −0.417597 − 0.908633i \(-0.637127\pi\)
−0.417597 + 0.908633i \(0.637127\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3.00000 0.155752
\(372\) 0 0
\(373\) 1.00000 0.0517780 0.0258890 − 0.999665i \(-0.491758\pi\)
0.0258890 + 0.999665i \(0.491758\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 12.0000 0.618031
\(378\) 0 0
\(379\) 37.0000 1.90056 0.950281 − 0.311393i \(-0.100796\pi\)
0.950281 + 0.311393i \(0.100796\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 36.0000 1.83951 0.919757 − 0.392488i \(-0.128386\pi\)
0.919757 + 0.392488i \(0.128386\pi\)
\(384\) 0 0
\(385\) −2.00000 −0.101929
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 12.0000 0.608424 0.304212 − 0.952604i \(-0.401607\pi\)
0.304212 + 0.952604i \(0.401607\pi\)
\(390\) 0 0
\(391\) −24.0000 −1.21373
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −1.00000 −0.0501886 −0.0250943 − 0.999685i \(-0.507989\pi\)
−0.0250943 + 0.999685i \(0.507989\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 10.0000 0.499376 0.249688 − 0.968326i \(-0.419672\pi\)
0.249688 + 0.968326i \(0.419672\pi\)
\(402\) 0 0
\(403\) 24.0000 1.19553
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.00000 0.0495682
\(408\) 0 0
\(409\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 12.0000 0.590481
\(414\) 0 0
\(415\) −6.00000 −0.294528
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −5.00000 −0.244266 −0.122133 − 0.992514i \(-0.538973\pi\)
−0.122133 + 0.992514i \(0.538973\pi\)
\(420\) 0 0
\(421\) 8.00000 0.389896 0.194948 − 0.980814i \(-0.437546\pi\)
0.194948 + 0.980814i \(0.437546\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −4.00000 −0.194029
\(426\) 0 0
\(427\) 4.00000 0.193574
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −10.0000 −0.481683 −0.240842 − 0.970564i \(-0.577423\pi\)
−0.240842 + 0.970564i \(0.577423\pi\)
\(432\) 0 0
\(433\) −39.0000 −1.87422 −0.937110 − 0.349034i \(-0.886510\pi\)
−0.937110 + 0.349034i \(0.886510\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 48.0000 2.29615
\(438\) 0 0
\(439\) −32.0000 −1.52728 −0.763638 − 0.645644i \(-0.776589\pi\)
−0.763638 + 0.645644i \(0.776589\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 13.0000 0.617649 0.308824 − 0.951119i \(-0.400064\pi\)
0.308824 + 0.951119i \(0.400064\pi\)
\(444\) 0 0
\(445\) 24.0000 1.13771
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −20.0000 −0.943858 −0.471929 − 0.881636i \(-0.656442\pi\)
−0.471929 + 0.881636i \(0.656442\pi\)
\(450\) 0 0
\(451\) 7.00000 0.329617
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −12.0000 −0.562569
\(456\) 0 0
\(457\) 18.0000 0.842004 0.421002 − 0.907060i \(-0.361678\pi\)
0.421002 + 0.907060i \(0.361678\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 6.00000 0.279448 0.139724 − 0.990190i \(-0.455378\pi\)
0.139724 + 0.990190i \(0.455378\pi\)
\(462\) 0 0
\(463\) −22.0000 −1.02243 −0.511213 − 0.859454i \(-0.670804\pi\)
−0.511213 + 0.859454i \(0.670804\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −18.0000 −0.832941 −0.416470 − 0.909149i \(-0.636733\pi\)
−0.416470 + 0.909149i \(0.636733\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −2.00000 −0.0919601
\(474\) 0 0
\(475\) 8.00000 0.367065
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 18.0000 0.822441 0.411220 − 0.911536i \(-0.365103\pi\)
0.411220 + 0.911536i \(0.365103\pi\)
\(480\) 0 0
\(481\) 6.00000 0.273576
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −16.0000 −0.726523
\(486\) 0 0
\(487\) −20.0000 −0.906287 −0.453143 − 0.891438i \(-0.649697\pi\)
−0.453143 + 0.891438i \(0.649697\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 − 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 0 0
\(493\) −8.00000 −0.360302
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −7.00000 −0.313993
\(498\) 0 0
\(499\) 4.00000 0.179065 0.0895323 − 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 8.00000 0.356702 0.178351 − 0.983967i \(-0.442924\pi\)
0.178351 + 0.983967i \(0.442924\pi\)
\(504\) 0 0
\(505\) 34.0000 1.51298
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −45.0000 −1.99459 −0.997295 − 0.0735034i \(-0.976582\pi\)
−0.997295 + 0.0735034i \(0.976582\pi\)
\(510\) 0 0
\(511\) 7.00000 0.309662
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 4.00000 0.176261
\(516\) 0 0
\(517\) 9.00000 0.395820
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 17.0000 0.744784 0.372392 − 0.928076i \(-0.378538\pi\)
0.372392 + 0.928076i \(0.378538\pi\)
\(522\) 0 0
\(523\) 6.00000 0.262362 0.131181 − 0.991358i \(-0.458123\pi\)
0.131181 + 0.991358i \(0.458123\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −16.0000 −0.696971
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 42.0000 1.81922
\(534\) 0 0
\(535\) 8.00000 0.345870
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 6.00000 0.258438
\(540\) 0 0
\(541\) −36.0000 −1.54776 −0.773880 − 0.633332i \(-0.781687\pi\)
−0.773880 + 0.633332i \(0.781687\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 32.0000 1.37073
\(546\) 0 0
\(547\) −8.00000 −0.342055 −0.171028 − 0.985266i \(-0.554709\pi\)
−0.171028 + 0.985266i \(0.554709\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 16.0000 0.681623
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −14.0000 −0.593199 −0.296600 − 0.955002i \(-0.595853\pi\)
−0.296600 + 0.955002i \(0.595853\pi\)
\(558\) 0 0
\(559\) −12.0000 −0.507546
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 22.0000 0.927189 0.463595 − 0.886047i \(-0.346559\pi\)
0.463595 + 0.886047i \(0.346559\pi\)
\(564\) 0 0
\(565\) −4.00000 −0.168281
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −28.0000 −1.17382 −0.586911 − 0.809652i \(-0.699656\pi\)
−0.586911 + 0.809652i \(0.699656\pi\)
\(570\) 0 0
\(571\) 21.0000 0.878823 0.439411 − 0.898286i \(-0.355187\pi\)
0.439411 + 0.898286i \(0.355187\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 6.00000 0.250217
\(576\) 0 0
\(577\) 32.0000 1.33218 0.666089 − 0.745873i \(-0.267967\pi\)
0.666089 + 0.745873i \(0.267967\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −3.00000 −0.124461
\(582\) 0 0
\(583\) −3.00000 −0.124247
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 24.0000 0.990586 0.495293 − 0.868726i \(-0.335061\pi\)
0.495293 + 0.868726i \(0.335061\pi\)
\(588\) 0 0
\(589\) 32.0000 1.31854
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −3.00000 −0.123195 −0.0615976 − 0.998101i \(-0.519620\pi\)
−0.0615976 + 0.998101i \(0.519620\pi\)
\(594\) 0 0
\(595\) 8.00000 0.327968
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −15.0000 −0.612883 −0.306442 − 0.951889i \(-0.599138\pi\)
−0.306442 + 0.951889i \(0.599138\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 − 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −20.0000 −0.813116
\(606\) 0 0
\(607\) 32.0000 1.29884 0.649420 − 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 54.0000 2.18461
\(612\) 0 0
\(613\) 35.0000 1.41364 0.706818 − 0.707395i \(-0.250130\pi\)
0.706818 + 0.707395i \(0.250130\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −9.00000 −0.362326 −0.181163 − 0.983453i \(-0.557986\pi\)
−0.181163 + 0.983453i \(0.557986\pi\)
\(618\) 0 0
\(619\) 5.00000 0.200967 0.100483 − 0.994939i \(-0.467961\pi\)
0.100483 + 0.994939i \(0.467961\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 12.0000 0.480770
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −4.00000 −0.159490
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 − 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −34.0000 −1.34925
\(636\) 0 0
\(637\) 36.0000 1.42637
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −31.0000 −1.22443 −0.612213 − 0.790693i \(-0.709721\pi\)
−0.612213 + 0.790693i \(0.709721\pi\)
\(642\) 0 0
\(643\) 14.0000 0.552106 0.276053 − 0.961142i \(-0.410973\pi\)
0.276053 + 0.961142i \(0.410973\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 36.0000 1.41531 0.707653 − 0.706560i \(-0.249754\pi\)
0.707653 + 0.706560i \(0.249754\pi\)
\(648\) 0 0
\(649\) −12.0000 −0.471041
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 8.00000 0.313064 0.156532 − 0.987673i \(-0.449969\pi\)
0.156532 + 0.987673i \(0.449969\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 21.0000 0.818044 0.409022 − 0.912525i \(-0.365870\pi\)
0.409022 + 0.912525i \(0.365870\pi\)
\(660\) 0 0
\(661\) −36.0000 −1.40024 −0.700119 − 0.714026i \(-0.746870\pi\)
−0.700119 + 0.714026i \(0.746870\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −16.0000 −0.620453
\(666\) 0 0
\(667\) 12.0000 0.464642
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −4.00000 −0.154418
\(672\) 0 0
\(673\) 11.0000 0.424019 0.212009 − 0.977268i \(-0.431999\pi\)
0.212009 + 0.977268i \(0.431999\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 15.0000 0.576497 0.288248 − 0.957556i \(-0.406927\pi\)
0.288248 + 0.957556i \(0.406927\pi\)
\(678\) 0 0
\(679\) −8.00000 −0.307012
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −42.0000 −1.60709 −0.803543 − 0.595247i \(-0.797054\pi\)
−0.803543 + 0.595247i \(0.797054\pi\)
\(684\) 0 0
\(685\) 28.0000 1.06983
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −18.0000 −0.685745
\(690\) 0 0
\(691\) 52.0000 1.97817 0.989087 − 0.147335i \(-0.0470696\pi\)
0.989087 + 0.147335i \(0.0470696\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −8.00000 −0.303457
\(696\) 0 0
\(697\) −28.0000 −1.06058
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −24.0000 −0.906467 −0.453234 − 0.891392i \(-0.649730\pi\)
−0.453234 + 0.891392i \(0.649730\pi\)
\(702\) 0 0
\(703\) 8.00000 0.301726
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 17.0000 0.639351
\(708\) 0 0
\(709\) 12.0000 0.450669 0.225335 − 0.974281i \(-0.427652\pi\)
0.225335 + 0.974281i \(0.427652\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 24.0000 0.898807
\(714\) 0 0
\(715\) 12.0000 0.448775
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.00000 −0.0372937 −0.0186469 − 0.999826i \(-0.505936\pi\)
−0.0186469 + 0.999826i \(0.505936\pi\)
\(720\) 0 0
\(721\) 2.00000 0.0744839
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2.00000 0.0742781
\(726\) 0 0
\(727\) −44.0000 −1.63187 −0.815935 − 0.578144i \(-0.803777\pi\)
−0.815935 + 0.578144i \(0.803777\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 8.00000 0.295891
\(732\) 0 0
\(733\) 19.0000 0.701781 0.350891 − 0.936416i \(-0.385879\pi\)
0.350891 + 0.936416i \(0.385879\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 21.0000 0.772497 0.386249 − 0.922395i \(-0.373771\pi\)
0.386249 + 0.922395i \(0.373771\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −43.0000 −1.57752 −0.788759 − 0.614703i \(-0.789276\pi\)
−0.788759 + 0.614703i \(0.789276\pi\)
\(744\) 0 0
\(745\) 18.0000 0.659469
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 4.00000 0.146157
\(750\) 0 0
\(751\) −33.0000 −1.20419 −0.602094 − 0.798426i \(-0.705667\pi\)
−0.602094 + 0.798426i \(0.705667\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 10.0000 0.363456 0.181728 − 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 27.0000 0.978749 0.489375 − 0.872074i \(-0.337225\pi\)
0.489375 + 0.872074i \(0.337225\pi\)
\(762\) 0 0
\(763\) 16.0000 0.579239
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −72.0000 −2.59977
\(768\) 0 0
\(769\) −10.0000 −0.360609 −0.180305 − 0.983611i \(-0.557708\pi\)
−0.180305 + 0.983611i \(0.557708\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −19.0000 −0.683383 −0.341691 − 0.939812i \(-0.611000\pi\)
−0.341691 + 0.939812i \(0.611000\pi\)
\(774\) 0 0
\(775\) 4.00000 0.143684
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 56.0000 2.00641
\(780\) 0 0
\(781\) 7.00000 0.250480
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 38.0000 1.35628
\(786\) 0 0
\(787\) −39.0000 −1.39020 −0.695100 − 0.718913i \(-0.744640\pi\)
−0.695100 + 0.718913i \(0.744640\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −2.00000 −0.0711118
\(792\) 0 0
\(793\) −24.0000 −0.852265
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −48.0000 −1.70025 −0.850124 − 0.526583i \(-0.823473\pi\)
−0.850124 + 0.526583i \(0.823473\pi\)
\(798\) 0 0
\(799\) −36.0000 −1.27359
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −7.00000 −0.247025
\(804\) 0 0
\(805\) −12.0000 −0.422944
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −26.0000 −0.914111 −0.457056 − 0.889438i \(-0.651096\pi\)
−0.457056 + 0.889438i \(0.651096\pi\)
\(810\) 0 0
\(811\) 45.0000 1.58016 0.790082 − 0.613001i \(-0.210038\pi\)
0.790082 + 0.613001i \(0.210038\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −44.0000 −1.54125
\(816\) 0 0
\(817\) −16.0000 −0.559769
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −29.0000 −1.01211 −0.506053 − 0.862502i \(-0.668896\pi\)
−0.506053 + 0.862502i \(0.668896\pi\)
\(822\) 0 0
\(823\) −24.0000 −0.836587 −0.418294 − 0.908312i \(-0.637372\pi\)
−0.418294 + 0.908312i \(0.637372\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 54.0000 1.87776 0.938882 − 0.344239i \(-0.111863\pi\)
0.938882 + 0.344239i \(0.111863\pi\)
\(828\) 0 0
\(829\) −40.0000 −1.38926 −0.694629 − 0.719368i \(-0.744431\pi\)
−0.694629 + 0.719368i \(0.744431\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −24.0000 −0.831551
\(834\) 0 0
\(835\) −24.0000 −0.830554
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −36.0000 −1.24286 −0.621429 − 0.783470i \(-0.713448\pi\)
−0.621429 + 0.783470i \(0.713448\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 46.0000 1.58245
\(846\) 0 0
\(847\) −10.0000 −0.343604
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 6.00000 0.205677
\(852\) 0 0
\(853\) 26.0000 0.890223 0.445112 − 0.895475i \(-0.353164\pi\)
0.445112 + 0.895475i \(0.353164\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 52.0000 1.77629 0.888143 − 0.459567i \(-0.151995\pi\)
0.888143 + 0.459567i \(0.151995\pi\)
\(858\) 0 0
\(859\) −32.0000 −1.09183 −0.545913 − 0.837842i \(-0.683817\pi\)
−0.545913 + 0.837842i \(0.683817\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) 6.00000 0.204006
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −12.0000 −0.405674
\(876\) 0 0
\(877\) −22.0000 −0.742887 −0.371444 − 0.928456i \(-0.621137\pi\)
−0.371444 + 0.928456i \(0.621137\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 30.0000 1.01073 0.505363 − 0.862907i \(-0.331359\pi\)
0.505363 + 0.862907i \(0.331359\pi\)
\(882\) 0 0
\(883\) 20.0000 0.673054 0.336527 − 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −47.0000 −1.57811 −0.789053 − 0.614325i \(-0.789428\pi\)
−0.789053 + 0.614325i \(0.789428\pi\)
\(888\) 0 0
\(889\) −17.0000 −0.570162
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 72.0000 2.40939
\(894\) 0 0
\(895\) 44.0000 1.47076
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 8.00000 0.266815
\(900\) 0 0
\(901\) 12.0000 0.399778
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −46.0000 −1.52909
\(906\) 0 0
\(907\) −32.0000 −1.06254 −0.531271 − 0.847202i \(-0.678286\pi\)
−0.531271 + 0.847202i \(0.678286\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 54.0000 1.78910 0.894550 − 0.446968i \(-0.147496\pi\)
0.894550 + 0.446968i \(0.147496\pi\)
\(912\) 0 0
\(913\) 3.00000 0.0992855
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −14.0000 −0.461817 −0.230909 − 0.972975i \(-0.574170\pi\)
−0.230909 + 0.972975i \(0.574170\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 42.0000 1.38245
\(924\) 0 0
\(925\) 1.00000 0.0328798
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −18.0000 −0.590561 −0.295280 − 0.955411i \(-0.595413\pi\)
−0.295280 + 0.955411i \(0.595413\pi\)
\(930\) 0 0
\(931\) 48.0000 1.57314
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −8.00000 −0.261628
\(936\) 0 0
\(937\) −19.0000 −0.620703 −0.310351 − 0.950622i \(-0.600447\pi\)
−0.310351 + 0.950622i \(0.600447\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −14.0000 −0.456387 −0.228193 − 0.973616i \(-0.573282\pi\)
−0.228193 + 0.973616i \(0.573282\pi\)
\(942\) 0 0
\(943\) 42.0000 1.36771
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 52.0000 1.68977 0.844886 − 0.534946i \(-0.179668\pi\)
0.844886 + 0.534946i \(0.179668\pi\)
\(948\) 0 0
\(949\) −42.0000 −1.36338
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 19.0000 0.615470 0.307735 − 0.951472i \(-0.400429\pi\)
0.307735 + 0.951472i \(0.400429\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 14.0000 0.452084
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −20.0000 −0.643823
\(966\) 0 0
\(967\) 34.0000 1.09337 0.546683 − 0.837340i \(-0.315890\pi\)
0.546683 + 0.837340i \(0.315890\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 32.0000 1.02693 0.513464 − 0.858111i \(-0.328362\pi\)
0.513464 + 0.858111i \(0.328362\pi\)
\(972\) 0 0
\(973\) −4.00000 −0.128234
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −4.00000 −0.127971 −0.0639857 − 0.997951i \(-0.520381\pi\)
−0.0639857 + 0.997951i \(0.520381\pi\)
\(978\) 0 0
\(979\) −12.0000 −0.383522
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 9.00000 0.287055 0.143528 − 0.989646i \(-0.454155\pi\)
0.143528 + 0.989646i \(0.454155\pi\)
\(984\) 0 0
\(985\) −14.0000 −0.446077
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −12.0000 −0.381578
\(990\) 0 0
\(991\) −22.0000 −0.698853 −0.349427 − 0.936964i \(-0.613624\pi\)
−0.349427 + 0.936964i \(0.613624\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −28.0000 −0.887660
\(996\) 0 0
\(997\) −6.00000 −0.190022 −0.0950110 − 0.995476i \(-0.530289\pi\)
−0.0950110 + 0.995476i \(0.530289\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 2664.2.a.f.1.1 1
3.2 odd 2 296.2.a.a.1.1 ✓ 1
4.3 odd 2 5328.2.a.o.1.1 1
12.11 even 2 592.2.a.c.1.1 1
15.14 odd 2 7400.2.a.f.1.1 1
24.5 odd 2 2368.2.a.n.1.1 1
24.11 even 2 2368.2.a.g.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
296.2.a.a.1.1 ✓ 1 3.2 odd 2
592.2.a.c.1.1 1 12.11 even 2
2368.2.a.g.1.1 1 24.11 even 2
2368.2.a.n.1.1 1 24.5 odd 2
2664.2.a.f.1.1 1 1.1 even 1 trivial
5328.2.a.o.1.1 1 4.3 odd 2
7400.2.a.f.1.1 1 15.14 odd 2